Sigma multiplicities for APN functions in dimensions up to 10
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For all known APN functions over GF(2^n) with n up to 10, the following tables list the partitions of GF(2^n) induced by the multiplicities of the Sigma sets <math>\Sigma_F^k(0)</sigma> for k = 4, as explained in the SETA paper on testing EA-equivalences.
Due to the large number of functions, the results for dimension 8 are listed on a separate page.
Dimension 9
Dimension 10
Functions 1-10 are indexed according to [[1]]. The remaining functions correspond to the ones found via self-equivalences, and are indexed in the same way as in the provided dataset.
| ID | Partition sizes |
|---|---|
| 1 | 1, 341, 682 |
| 2 | 1, 341, 682 |
| 3 | 1, 341, 682 |
| 4 | 1, 341, 682 |
| 5 | 1, 341, 682 |
| 6 | 1, 341, 682 |
| 7 | 1, 341, 682 |
| 8 | 1, 341, 682 |
| 9 | 1, 341, 682 |
| 10 | 1, 341, 682 |
| 11 | 1, 341, 682 |
| 12 | 1, 341, 682 |
| 13 | 1, 341, 682 |
| 14 | 1, 341, 682 |
| 15 | 1, 341, 682 |
| 16 | 1, 341, 682 |
| 17 | 1, 31, 155, 155, 155, 217, 310 |
| 18 | 1, 341, 682 |
| 19 | 1, 124, 217, 310, 372 |
| 20 | 1, 341, 682 |
| 21 | 1, 11, 11, 165, 330, 506 |